The chin has an eye injury. The cornea may be scratched. These injuries heal most of the time, but sometimes the eye will stay that way or not completely uncloud.
If there is no infection, there's really nothing a vet can do. I would suggest keeping it cleaned up. It most likely didn't turn white from an infection...it takes a nice eye injury to get it like that - like a really good poke to the eye or the chin running into something, etc. The eyeball is swollen.
I had a vet explain the mechanism by which this occurs. It has something to do with the cornea taking on water or moisture or something. I can't remember exactly. It turns white because it is healing up. That vet never suggested antibiotics for it because it wasn't a sign of infection.
The thing that I would really worry about is if the chin hit it's head or nose and damaged the sinus cavity in some way.
If it IS from an infection, the chin probably has an upper respiratory infection that has spread to the eyes and ears. It sounds like it's probably an injury in this case. Without wheezing or any signs that there's something wrong, I'd say that a regularly scheduled vet visit would be in order - an emergency visit probably isn't necessary.